Individual-scale analysis

Pair-wise correlations

Between continuous variables: Pearson
Between a binary and a continuous variable: Mann-Whitney
Between binary variables: Chi-square

Latitude

Age

Altitud

BMI

Diabetes

Hypertension

Sugar

Vitamin D

Multiple regression 1

Response variable = vit D
Explanatory variables = bmi, lat, alt
Only using data of women 20-49 (no BMI data for > 60)

## 
## Call:
## lm(formula = vitD ~ scale(BMI) + scale(Lat) + scale(Altitude), 
##     data = df_20_50)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -49.186 -11.162  -1.078   9.929  78.566 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      61.1982     0.3383 180.921   <2e-16 ***
## scale(BMI)       -2.9808     0.3408  -8.746   <2e-16 ***
## scale(Lat)       -3.8711     0.3432 -11.279   <2e-16 ***
## scale(Altitude)  -5.6014     0.3474 -16.124   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.56 on 2393 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.1371, Adjusted R-squared:  0.136 
## F-statistic: 126.7 on 3 and 2393 DF,  p-value: < 2.2e-16

Multiple regression 2

Response variable = vit D
Explanatory variables = lat, alt
Using all data (ages 20 - > 60)

## 
## Call:
## lm(formula = vitD ~ scale(Lat) + scale(Altitude), data = df_20_60)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -58.880 -11.834  -1.393  10.236 129.025 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      61.6521     0.3072  200.68   <2e-16 ***
## scale(Lat)       -3.8095     0.3122  -12.20   <2e-16 ***
## scale(Altitude)  -5.4344     0.3122  -17.41   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.46 on 3227 degrees of freedom
## Multiple R-squared:  0.1076, Adjusted R-squared:  0.107 
## F-statistic: 194.5 on 2 and 3227 DF,  p-value: < 2.2e-16

Municipal-scale analysis

Using only women 20-49 dataset

Pair-wise correlations

Deaths per 100,000

Altitude

Latitude

Ethnicity

Mean Vit D

nmol < 30

nmol < 50

nmol < 75

Multivariate regression 0

Response variable = vit D
Explanatory variables = Altitude and Latitude

Unscaled variables

The coefficient value (column "Estimate") represents the mean change of deaths/ht given a one-unit shift in the independent variable

## 
## Call:
## lm(formula = mean_vitD ~ Alt + Lat, data = df_mun)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.9712  -3.9240   0.3683   3.4497  18.8023 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 87.9558348  2.8874294  30.462  < 2e-16 ***
## Alt         -0.0065317  0.0005223 -12.506  < 2e-16 ***
## Lat         -0.9283350  0.1233005  -7.529 4.88e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.612 on 146 degrees of freedom
## Multiple R-squared:  0.551,  Adjusted R-squared:  0.5449 
## F-statistic: 89.59 on 2 and 146 DF,  p-value: < 2.2e-16

Scaled variables

The coefficient value (column "Estimate") represents the mean change of deaths/ht given a one-std-deviation shift in the independent variable (indicates which variable has a bigger effect on deaths/ht).

## 
## Call:
## lm(formula = mean_vitD ~ scale(Alt) + scale(Lat), data = df_mun)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.9712  -3.9240   0.3683   3.4497  18.8023 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  61.3983     0.4597 133.558  < 2e-16 ***
## scale(Alt)   -5.9286     0.4741 -12.506  < 2e-16 ***
## scale(Lat)   -3.5692     0.4741  -7.529 4.88e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.612 on 146 degrees of freedom
## Multiple R-squared:  0.551,  Adjusted R-squared:  0.5449 
## F-statistic: 89.59 on 2 and 146 DF,  p-value: < 2.2e-16

Variance Inflation factor

Confirms collinearity in the model. VIF = 1 is best. VIF > 5 means problematic variable (correlated with other(s))

##  Alt  Lat 
## 1.06 1.06

Multivariate regression 1

Response variable = Deaths per 100,000
Explanatory variables = Altitude and Latitude

Unscaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.684 -10.062  -1.104   6.567  59.323 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -19.261431   8.301666  -2.320   0.0217 *  
## Alt           0.003873   0.001502   2.579   0.0109 *  
## Lat           2.038969   0.354502   5.752    5e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.13 on 146 degrees of freedom
## Multiple R-squared:  0.1922, Adjusted R-squared:  0.1811 
## F-statistic: 17.37 on 2 and 146 DF,  p-value: 1.712e-07

Scaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ scale(Alt) + scale(Lat), data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.684 -10.062  -1.104   6.567  59.323 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   28.988      1.322  21.932   <2e-16 ***
## scale(Alt)     3.515      1.363   2.579   0.0109 *  
## scale(Lat)     7.839      1.363   5.752    5e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.13 on 146 degrees of freedom
## Multiple R-squared:  0.1922, Adjusted R-squared:  0.1811 
## F-statistic: 17.37 on 2 and 146 DF,  p-value: 1.712e-07

Variance Inflation factor

##  Alt  Lat 
## 1.06 1.06

Multivariate regression 2

Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude, nmol < 30

Unscaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat + nmol_30, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.308  -9.256  -1.324   7.033  56.424 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -14.954767   8.242257  -1.814  0.07168 .  
## Alt           0.002704   0.001521   1.778  0.07758 .  
## Lat           1.775510   0.358072   4.959 1.96e-06 ***
## nmol_30      88.748859  30.976930   2.865  0.00479 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.75 on 145 degrees of freedom
## Multiple R-squared:  0.2355, Adjusted R-squared:  0.2197 
## F-statistic: 14.89 on 3 and 145 DF,  p-value: 1.683e-08

Scaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ scale(Alt) + scale(Lat) + scale(nmol_30), 
##     data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.308  -9.256  -1.324   7.033  56.424 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      28.988      1.290  22.467  < 2e-16 ***
## scale(Alt)        2.455      1.381   1.778  0.07758 .  
## scale(Lat)        6.826      1.377   4.959 1.96e-06 ***
## scale(nmol_30)    3.926      1.370   2.865  0.00479 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.75 on 145 degrees of freedom
## Multiple R-squared:  0.2355, Adjusted R-squared:  0.2197 
## F-statistic: 14.89 on 3 and 145 DF,  p-value: 1.683e-08

Variance Inflation factor

##     Alt     Lat nmol_30 
##    1.14    1.13    1.12

Multivariate regression 3

Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude, nmol < 30, ethnicity

Unscaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat + nmol_30 + Ethnicity, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.970  -8.453  -1.360   6.921  56.281 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -11.752762  11.479530  -1.024 0.307646    
## Alt           0.002520   0.001593   1.582 0.115843    
## Lat           1.675417   0.436992   3.834 0.000188 ***
## nmol_30      88.968012  31.071660   2.863 0.004819 ** 
## Ethnicity    -0.043904   0.109218  -0.402 0.688293    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.8 on 144 degrees of freedom
## Multiple R-squared:  0.2363, Adjusted R-squared:  0.2151 
## F-statistic: 11.14 on 4 and 144 DF,  p-value: 6.682e-08

Scaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ scale(Alt) + scale(Lat) + scale(nmol_30) + 
##     scale(Ethnicity), data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.970  -8.453  -1.360   6.921  56.281 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       28.9878     1.2940  22.402  < 2e-16 ***
## scale(Alt)         2.2877     1.4461   1.582 0.115843    
## scale(Lat)         6.4415     1.6801   3.834 0.000188 ***
## scale(nmol_30)     3.9355     1.3744   2.863 0.004819 ** 
## scale(Ethnicity)  -0.6455     1.6058  -0.402 0.688293    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.8 on 144 degrees of freedom
## Multiple R-squared:  0.2363, Adjusted R-squared:  0.2151 
## F-statistic: 11.14 on 4 and 144 DF,  p-value: 6.682e-08

Variance Inflation factor

##       Alt       Lat   nmol_30 Ethnicity 
##      1.24      1.67      1.12      1.53

Municipal-scale analysis

Multivariate regression

Using only women > 60 dataset
Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude

Unscaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat, data = df_mun_60)
## 
## Residuals:
##       1       2       3       4       5       6       7 
##  107.21 -124.92  195.27 -179.42  243.27  -72.88 -168.52 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -2.417e+03  1.037e+03  -2.332   0.0801 .
## Alt         -7.699e-02  1.110e-01  -0.694   0.5260  
## Lat          1.552e+02  5.339e+01   2.908   0.0438 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 218.1 on 4 degrees of freedom
## Multiple R-squared:  0.7031, Adjusted R-squared:  0.5547 
## F-statistic: 4.737 on 2 and 4 DF,  p-value: 0.08814

Scaled variables

## 
## Call:
## lm(formula = Deaths_ht ~ scale(Alt) + scale(Lat), data = df_mun_60)
## 
## Residuals:
##       1       2       3       4       5       6       7 
##  107.21 -124.92  195.27 -179.42  243.27  -72.88 -168.52 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   667.64      82.44   8.098  0.00126 **
## scale(Alt)    -72.98     105.20  -0.694  0.52604   
## scale(Lat)    305.89     105.20   2.908  0.04378 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 218.1 on 4 degrees of freedom
## Multiple R-squared:  0.7031, Adjusted R-squared:  0.5547 
## F-statistic: 4.737 on 2 and 4 DF,  p-value: 0.08814